Particle acceleration based on high intensity laser systems (a process known as laser-plasma acceleration) has achieved high quality particle beams that compare favourably with conventional acceleration techniques in terms of emittance, brightness and pulse duration. A long-term difficulty associated with laser-plasma acceleration--the very broad, exponential energy spectrum of the emitted particles--has been overcome recently for electron beams. Here we report analogous results for ions, specifically the production of quasi-monoenergetic proton beams using laser-plasma accelerators. Reliable and reproducible laser-accelerated ion beams were achieved by intense laser irradiation of solid microstructured targets. This proof-of-principle experiment serves to illuminate the role of laser-generated plasmas as feasible particle sources. Scalability studies show that, owing to their compact size and reasonable cost, such table-top laser systems with high repetition rates could contribute to the development of new generations of particle injectors that may be suitable for medical proton therapy.